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On 8/18/2011 7:24 AM, Bruno Marchal wrote:

I agree with that sentiment. That's why I often try to think of
consciousness in terms of what it would mean to provide a Mars
Rover with consciousness. According to Bruno the ones we've sent
to Mars were already conscious, since their computers were capable
of Lobian logic.

I don't remember having said this. I even doubt that Mars Rover is
universal, although that might be serendipitously possible
(universality is very cheap), in which case it would be as
conscious as a human being under a high dose of salvia (a form of
consciousness quite disconnected from terrestrial realities). But
it is very probable that it is not Löbian. I don't see why they
would have given the induction axioms to Mars Rover (the induction
axioms is what gives the Löbian self-referential power).

You didn't say it explicitly. It was my inference that the
computer's learning algorithms would include induction.

Yes, and that makes them universal. To make them Löbian, you need them
to not just *do* induction, but they have to believe in induction.

Roughly speaking. If *i* = "obeys the induction rule", For a UM *i*
is true, but that's all. For a LUM is is not just that *i* is true,
but *i*is believed by the machine. For a UM *i* is true but B*i* is
false. For a LUM we have both *i* is true, and B*i* is true.

Of course the induction here is basically the induction on numbers(*).
It can be related to learning, anticipating or doing inductive
inference, but the relation is not identity.

(*) The infinity of axioms: F(0) & for all n (P(n) -> P(s(n)) ->.
for all n P(n).
With F any arithmetical formula, that is a formula build with the
logical symbol, and the arithmetical symbols {0, s, +, *}.

Brent
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